The solution of the wave equation for the scattering of particles by a coulombian centre of force

Abstract

The problem of the scattering of a stream of charged particles by a Coulombian centre of force has been treated by Wentzel and by Oppenheimer, who use Born’s method of successive approximations. They have shown that, if ZZ' ε 2 / hv is small, the quantum theory gives the well-known Rutherford formula. Furthermore, if ZZ' ε 2 / hv is large, we know that the quantum theory result must tend towards the classical, and it seemed probable that the two theories would agree for intermediate values of this constant. In this paper we shall show that this is actually the case. We shall first consider the more general problem of scattering by a field V( r ). The wave equation is ∇ 2 ϕ +2 m / h 2 (E - V) ϕ = 0. (1)